Identification & What Makes the Result Tight (aejmic-identification)

AEJ: Micro is theory-first, so "identification" here is two things. For pure theory it means: which assumptions are doing the work, and how tight/robust the mechanism is. For structural and experimental work it means the standard data-to-object mapping. Pick the branch.

When to trigger

(Theory) A referee asks whether the result is a knife-edge artifact of one assumption
(Theory) You cannot say cleanly which primitive drives the comparative static
(Structural) Parameters are estimated but it is unclear what in the data identifies them
(Experimental) The estimand or the assumptions behind the treatment effect are not pinned down

Branch A: Pure theory — what makes the result tight

The AEJ: Micro bar is that the reader sees exactly which assumption is load-bearing and how far the mechanism extends.

Decompose the assumptions. For each substantive assumption, ask: is the result false without it, weaker without it, or unchanged (then it was WLOG — say so)? The result is "tight" when you can name the assumption that breaks it.
Comparative statics as identification. Show the sign/magnitude of the key comparative static and what primitive drives it (single-crossing? a supermodularity? a curvature condition?). Monotone-comparative-statics tools (Topkis, Milgrom–Shannon) make the driver explicit.
Necessity, not just sufficiency. Where you can, show the assumption is necessary (a counterexample when it fails), not merely sufficient — this is what makes a characterization tight.
Robustness of the mechanism (then hand to aejmic-robustness for full extensions): does the result survive a small perturbation of the information structure, the timing, or the type distribution?

Branch B: Structural / empirical IO

Name what identifies each parameter. Tie parameters to specific data features / moments; argue identification from the model's structure, not "the estimator converged."
Targeted vs. untargeted moments; report a sensitivity/informativeness measure so readers see which data move which parameters.
Estimation regularity: objective (MLE/GMM/MSM), starting values, tolerances, multi-start; Monte Carlo recovery of known parameters.
Counterfactual validity: argue the estimated parameters are policy-invariant enough for the counterfactual (Lucas critique).
For reduced-form companions, use design-appropriate diagnostics (pre-trends, first-stage strength, density tests) and report SEs, not asterisks.

Branch C: Experimental (theory-grounded)

Design maps to the model: each treatment isolates a model primitive or prediction; state the estimand.
Pre-registration in a recognized registry where applicable; report deviations; include instructions/transcripts.
Randomization balance; attrition (Lee bounds if differential); multiple-hypothesis adjustment; external-validity scope.

Execution bridge (StatsPAI / Stata MCP)

Estimate and audit the identification claim, don't only argue it. Full map: execution-with-mcp. AEJ: Micro spans applied and structural micro; the chain below is for the reduced-form / causal lane — structural estimation uses the field's own solvers.

detect_design → recommend → fit with as_handle=true → audit_result to list the checks the design still owes.
Staggered DiD: callaway_santanna / sun_abraham + bacon_decomposition + honest_did_from_result (the pre-trend test is low-power, Roth 2022).
IV: effective_f_test + an anderson_rubin_ci (valid under weak instruments), not a 2SLS t-stat alone.
RDD: rdrobust (bias-corrected) + rddensity / mccrary_test for manipulation.
OVB: oster_delta / sensemakr — how strong a confounder would have to be.

Report the economic magnitude; route the full battery to the appendix; keep every number reproducible. A run end-to-end (synthetic data, real returns) is in the JF execution walkthrough. If StatsPAI/Stata are not connected, adapt the vendored resources/code/ skeleton and flag any unverified number.

Checklist

[ ] Branch chosen; the "what makes it tight / what identifies it" question answered in one sentence
[ ] Theory: each substantive assumption classified (false/weaker/WLOG without it); the load-bearing one named
[ ] Theory: key comparative static signed with its driving primitive; necessity shown where possible
[ ] Structural: each parameter tied to identifying moments; sensitivity + Monte Carlo recovery
[ ] Experimental: estimand stated; pre-registered; balance/attrition/MHT handled
[ ] Inference (applied): SEs / coverage sets, never asterisks; clustering correct

Anti-patterns

(Theory) A result whose driving assumption is never identified — "it just works"
(Theory) Claiming a characterization is tight without a counterexample when the assumption fails
(Structural) "The estimator converged" presented as identification
(Structural) A counterfactual on calibrated parameters with no policy-invariance argument
(Experimental) No pre-registration or no stated estimand; significance asterisks instead of SEs

Worked vignette (illustrative)

A matching paper proves stability is preserved under a new preference domain. A referee suspects it rides on a substitutability condition. The AEJ: Micro answer names it: "Substitutability is load-bearing — without it, Example 3 exhibits an empty core; with the weaker 'unilateral substitutes' condition the existence result survives but uniqueness fails." That sentence makes the result tight: the necessary assumption is named, and the cost of relaxing it is shown.

Output format

【Branch】theory / structural / experimental
【What makes it tight / data-to-object】one sentence
【Load-bearing assumption(s) or identifying moments】[...]
【Tightness evidence】counterexample-on-failure / sensitivity+Monte Carlo / balance+estimand
【What it does NOT establish】[...]
【Next step】aejmic-robustness (extensions/edge cases)